Graphite has a spherical and flake like shape in Ductile and gray Iron respectively. There is a little coherency between graphite and Iron matrix so many researchers considered graphite as a crack in the Iron. When the graphite has a circular morphology in 2D under microscope it means that stress concentration factor is much more lower than the one for grey Iron. Because of this, it is suggested to use Ductile Iron in load bearing application.
Machine tool needs precision, then thermal and structural stability. Grey will ease vibration absorption, but you also have to focus on the architecture and the geometry of your machine body.
The manufacturing of the machine tool structure could also impact your material choice (or the reverse) and the prices.
Thank you Mr Perry. You are right that we also need to look at the thermal and structural properties. However, the question is regarding Vibration absoption.
For the thermal expansion, both Grey Cast Iron and Ductile Iron have almost same thermal expansion coefficient. Though it is obvious that the tensile strength for the Ductile Iron is far better than Grey Cast Iron.
Ductile Iron as the name suggests is very ductile in nature and is therefore pretty flex. Its tensile strength is about 413.7 MPa and therefore, it is widely used for manufacturing machine parts which require higher strength. But Gray iron although brittle, has excellent damping characteristics. Hence, gray iron would be a better choice to resist vibrations. Although I do not believe a machine will be manufactured of any one of these materials solely. Areas in the machine tool need to be undergone modal analysis to obtain the tool's natural frequency and modes of vibrations and areas with greater influence of vibrations due to the source of vibrations should be made of gray iron and areas requiring higher strength must be casted off ductile iron.